1. Introduction to Kinematics
Unit 1 Presentation 3

2. What is Kinematics?
Kinematics: The study of motion without regard to its cause
Constant or Zero Acceleration
Kinematic motion can be described by six basic equations

3. Six Basic Kinematic Equations

4. Some Definitions Scalar: Magnitude Only (No direction)
Vector: Magnitude + Direction
Everything in Physics is either a Scalar or a Vector
Never both and never neither!

5. Distance vs. Displacement
Distance is a scalar
Total distance covered, no regard to direction
Displacement is a vector
Change in position, WITH regards to direction. Always a linear, one-directional change.

6. Distance vs. Displacement
Lets say Mr. Hamm walks from the Initial Position to the Final Position along the blue arrows. That is his PATH, and the distance covered is the total length of the two arrows.
Final Position
The displacement of Mr. Hamm is represented by the red arrow, and is equal to the length of that one arrow and the direction of the arrow (represented by a bearing).
Displacement is always less than or equal to distance.
Initial Position

7. Speed vs. Velocity Speed is a scalar Velocity is a vector
Speed: change in distance divided by the change in time
Velocity is a vector
Velocity: change in displacement divided by the change in time.
Velocity has a magnitude and a direction.

8. Speed and Velocity
Average velocity is NOT the same as average speed. If you run from x=0 m to x=25 m and then back again to x=0 m in 5 seconds, your average velocity is zero (displacement is zero), which your average speed is 10 m/s.

9. Average vs. Instantaneous
Velocity can be found by calculating the slope on a displacement vs. time graph.
Velocity AT a specific time
(ti in this case)
Average Velocity:
Slope of Secant Line
Average velocity over a certain time interval (to to tf) to ti tf

10. Acceleration Acceleration is always a vector
Acceleration can be average (over a time interval) or instantaneous (at a specific time)

11. Meter per second squared (m/s2)
SI Units
Measurement
SI Unit
Distance
Meter (m)
Displacement
Speed
Meter per second (m/s)
Velocity
Acceleration
Meter per second squared (m/s2)
Time
Second

12. Graph Analysis Example
A particle moves along the x-axis according to the graph on the left.
What is the average velocity of the particle in the time interval 1 < t < 5 seconds?
To find the average velocity, we must find the slope of the line in this interval.
Slope =
Hence, the average velocity over this time interval is 1 m/s.

13. Displacement Can we have negative displacement? YES!!!
For example, the particle in the last example moves from position x=0 m to x=-4 m (moves to the left instead of the right).
The negative sign represents the “negative” direction of the displacement. The magnitude of the motion is still 4 meters, just in the “negative” direction. Remember, vectors are magnitude AND direction!
See the next example.

14. Another Graph Analysis Example
A particle moves along the x-axis according to the graph on the left.
What is the average velocity of the particle in the time interval 6 < t < 8 seconds?
To find the average velocity, we must find the slope of the line in this interval.
Slope =
Hence, the velocity is -4 m/s. Since this value is negative, the particle must be moving to the LEFT, or along the negative x-axis, which is true.

15. Another Graph Example
A particle moves along the x-axis with a velocity according to the graph on the left.
What is the average acceleration of the particle in the time interval 1 < t < 4 seconds?
To find the average velocity, we must find the slope of the line in this interval.
Slope =
Hence, the average acceleration over this time interval is 2 m/s2.